Collaborative Research: Generalized Fiducial Inference in the Age of Data Science

协作研究：数据科学时代的广义基准推理

基本信息

批准号：
1916115
负责人：
Jan Hannig
金额：
$ 15万
依托单位：
University of North Carolina at Chapel Hill
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1916115&HistoricalAwards=false
关键词：
Collaborative Research Generalized Fiducial Inference

项目摘要

Data and their use have become extremely important in modern society. This provides for an urgent need to study mathematical foundations of statistics and data science. In this project the PIs explore interaction of generalized fiducial inference with modern data science problems and techniques. There are several benefits of the proposed research. First, it is expected that the proposed research will increase our understanding of inference and relationships between the frequentist, fiducial and Bayesian paradigms and how do these paradigms fit into data science which the aim to improve better data science practice. Second, it is expected to lead to new and efficient procedures for quantifying uncertainty in a number of applications. An important example is the calibration of likelihood ratios reported by data science algorithms in forensic science that has potential implication for practical usage of likelihood ratios in courtroom. Additionally, the project will provide research opportunities to graduate students and, in particular, help train women and minority graduate students in the field that is of a great benefit to society.Beginning around the year 2000, the PIs and collaborators started to re-investigate the ideas of fiducial inference and discovered that Fisher's approach, when properly generalized, opens doors to solve many important and difficult problems of uncertainty quantification. After many years of preliminary investigations, the team was able to put together a coherent, well thought out plan for a systematic research program in this area. The PIs termed their generalization of Fisher's ideas as generalized fiducial inference (GFI). The PIs are now working towards applying their GFI methodology to handle data science problems that have emerged due to our ability to collect massive amounts of data rapidly. In particular the PIs propose to conduct research into the following topics: (1) In-depth investigation of fundamental issues of GFI so that they can be simply used on manifolds, with constraint, and penalties. This is essential for applicability. (2) Development of a bias free fiducial selector, so that a sparsity of the fiducial distribution is induced as a natural outcome of a minimization problem and unbiasedness is achieved using a novel de-biasing approach. (3) Interplay between objective Bayesian and fiducial solutions for covariance estimation. (4) Uncertainty quantification for graphon and regression with network cohesion. (5) Use of deep networks for computation of GFI. (6) Applications of GFI to a wide variety of practical problems; e.g., calibration of likelihood ratios used for quantifying evidence in forensic science.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

数据和它们的使用在现代社会中变得极为重要。这迫切需要研究统计和数据科学的数学基础。在这个项目中，PIS探索了普遍的基准推断与现代数据科学问题和技术的相互作用。拟议的研究有几个好处。首先，预计拟议的研究将增加我们对频繁，信托和贝叶斯范式之间的推论和关系的理解，以及这些范式如何适合数据科学，旨在改善更好的数据科学实践。其次，预计将导致新的有效的程序来量化许多应用程序中的不确定性。一个重要的例子是，法医学中数据科学算法报告的似然比校准对法庭中的似然比实际使用有潜在的影响。此外，该项目将为研究生提供研究机会，尤其是帮助培训该领域的妇女和少数族裔研究生，这对社会有益于社会。在2000年左右，PIS和合作者开始重新研究基督的思想，并在适当的普遍性和难以确定的量化方面发现了Fisher的方法，并发现Fisher的方法解决了许多重要的问题。经过多年的初步调查，该团队能够为该领域的系统研究计划制定一个连贯，经过深思熟虑的计划。 PIS称他们对Fisher的思想的概括是普遍的基准推断（GFI）。 PI现在正在努力应用其GFI方法来处理由于我们能够快速收集大量数据的能力而出现的数据科学问题。特别是PI提议对以下主题进行研究：（1）对GFI基本问题的深入研究，以便可以将其简单地用于流形，限制和惩罚。这对于适用性至关重要。（2）发展无偏见的基准选择者，因此，通过新颖的偏见方法来诱导基准分布的稀疏性作为最小化问题和无偏见的自然结果。（3）客观贝叶斯和基准解决方案之间的相互作用以进行协方差估计。（4）Graphon的不确定性定量和具有网络凝聚的回归。（5）使用深网计算GFI。（6）GFI在各种实际问题上的应用；例如，该奖项反映了NSF的法定任务，该奖项反映了NSF的法定任务，并且被认为是值得通过基金会的知识分子优点和更广泛的影响评估标准来评估的。